An important strand of research in behavioural finance asks the question whether mispricings in financial markets (usually represented by irrational traders or sentiment) affect the financing and investment decisions of firms. Clearly, as Morck, Shleifer and Vishny [16] put it, if the stock market were [only] a sideshow, market inefficiencies would merely redistribute wealth between smart investors and noise traders and would not have feed back effects to investments at all. However, if stock prices influence real economic activity, then irrational traders can indirectly affect real activity as well.
The question how a rational manager, interested in maximizing firm value, should act when facing irrational investors has been tackled by Stein [27]. He shows that when a firms stock price is too high, a rational manager should issue more shares and take advantage of the mispricing, and when the price is too low, she should repurchase shares. Regarding what to do with the fresh capital, he also shows that non equity dependent firms should not invest straight to any investment opportunities but instead keep the money raised in cash. However, for equity dependent firms, market mispricing could matter and could also distort investment decisions. If, for example, a firm has to raise capital for new investments in an underpriced market, they may have to forgo attractive opportunities because it is too costly to finance them with undervalued equity. On the flip side, if a rational manager refuses to to undertake projects irrational investors percieve as profitable but actually they are not, they may depress stock prices or have him fired.The above stories lead to the prediction that investments of equity$dependent firms should positively correlate with stock mispricings.
This paper provides a different approach to capture the correlation between mispricing and investment by studying the effect of short sale constraints on coordination among capital providers for a real investment. Capital providers with dispersed information consider whether or not to invest in a project, and they use an (endogenous) public signal in the form of a market price to coordinate their actions. The market price is informative about the quality of the project as it reflects the information of speculators who are endowed with private signals about this project. I examine the effect of short sale constraints (in the market) on investments and market prices. The model consists of two parallel games: the market, where speculators operate, is a noisy REE model with or without short sale constraints. The second phase is an investment round, where capital providers consider investing in a project. The project is undertaken if the aggregate investment is sufficiently large, and investors payoff is higher if the project is successful. It is in fact a coordination game, in the spirit of standard global games, with private and public information. Finally, the investment size affects the final payoff of the risky asset traded in the market.
In a simple financial market model, the introduction of short sale constraints increases the price volatility as they increase potential uninformed traders perceived uncertainty about the asset payoff by decreasing the information content of the market price. This increased price volatility means weaker information content of the public signal of investors. Unlike standard global games with public and private information, this model shows that multiplicity in the investment size and outcome prevails under short sale constraints as the important feature is not the increased volatility but the fact that volatility increases asymmetrically. Multiplicity in investment leads to multiplicity in the price too, when investment has a feedback effect on the asset dividend. Therefore short sale constraints might create large price jumps or falls not simply as a result of an increase in perceived uncertainly but as a result of affecting coordination.
The backbone of the present paper is a standard coordination game in the spirit of Morris and Shin [17], and builds in particular on the strand studying the interaction between private and public information (see, for example, Morris and Shin [18], [19], [20] and [21]). These models show that Atkeson [4] discusses the potential role of financial markets as the sources of endogenous public information, formalized by Angeletos and Werning [3]. They incorporate a standard Grossman and Stiglitz [11] financial market where agents with dispersed information interact, and use the rational expectations equilibrium price as public information. They show that a unique equilibrium might not emerge as a small perturbation from perfect information, due to the endogenous nature of the public signal. This paper builds on their analysis in treating the market price as a public signal, but instead focuses on the effect of introducing portfolio constraints on market participants. Therefore, the main difference is that multiplicity does not arise because the public information gets more precise when improving the quality of private information, but only because short$sale constraints confuse investors, who are not sure to what extent these constraints bind. Indeed, in the Angeletos and Werning [3] sense, the market price is exogenous, and absent any constraints, the present model simplifies to that of Morris and Shin [19] and [21].
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Coordination and real investments under short sale constraints
